Properties

Label 25.2
Level 25
Weight 2
Dimension 12
Nonzero newspaces 2
Newforms 2
Sturm bound 100
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(100\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(25))\).

Total New Old
Modular forms 39 33 6
Cusp forms 12 12 0
Eisenstein series 27 21 6

Trace form

\(12q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 18q^{12} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut -\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 4q^{18} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 10q^{20} \) \(\mathstrut -\mathstrut 6q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 20q^{24} \) \(\mathstrut -\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 18q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut +\mathstrut 23q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 6q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 25q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 36q^{48} \) \(\mathstrut -\mathstrut 8q^{49} \) \(\mathstrut -\mathstrut 25q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 22q^{52} \) \(\mathstrut -\mathstrut q^{53} \) \(\mathstrut -\mathstrut 20q^{54} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut +\mathstrut 30q^{70} \) \(\mathstrut +\mathstrut 14q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 10q^{75} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 28q^{78} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 27q^{81} \) \(\mathstrut -\mathstrut 4q^{82} \) \(\mathstrut -\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 35q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 25q^{90} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut -\mathstrut 26q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 14q^{96} \) \(\mathstrut -\mathstrut 52q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
25.2.a \(\chi_{25}(1, \cdot)\) None 0 1
25.2.b \(\chi_{25}(24, \cdot)\) None 0 1
25.2.d \(\chi_{25}(6, \cdot)\) 25.2.d.a 4 4
25.2.e \(\chi_{25}(4, \cdot)\) 25.2.e.a 8 4